Efficient matrix-free GPU implementation of Fixed Grid Finite Element Analysis

Martínez-Frutos, Jesús; Herrero-Pérez, David

doi:10.1016/j.finel.2015.06.005

Cited by 29 publications

(21 citation statements)

References 47 publications

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“…It was shown in the context of elasticity problems that synchronization overhead from graph coloring is more costly than the unfavorable memory access patterns which it prevents, especially for 3D problems. Martínez-Frutos and Herrero-Pérez further explored the DbD method for elasticity problems on a fixed grid mesh so that only one local finite element matrix is required [20]. By varying material coefficients at the element level, between a constant "inside" and zero "outside", different domain geometries were enforced on the same mesh.…”

Section: Background and Motivationmentioning

confidence: 99%

“…The construction of a Jacobi preconditioner is a straightforward process that lends itself to element-wise parallel computation. We note that the development of preconditioners that can be computed on a GPU is an active area of research [20,8], but is not a focus of the present study. A comparison of this strategy with a serial implementation having a stronger preconditioner is made in Section 5.3.…”

Section: Preconditioned Conjugate Gradientmentioning

confidence: 99%

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Analysis of heterogeneous computing approaches to simulating heat transfer in heterogeneous material

Loeb

Earls

2019

Journal of Parallel and Distributed Computing

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The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having simple geometries. The finite element method can provide approximations to a weak form continuum solution, with increasing accuracy as the number of degrees of freedom in the model increases. This comes at a cost of increased memory usage and computation time; even when taking advantage of sparse matrix techniques for the finite element system matrix. We summarize recent approaches in solving problems in structural mechanics and steady state heat conduction which do not require the explicit assembly of any system matrices, and adapt them to a method for solving the time-depended flow of heat. These approaches are highly parallelizable, and can be performed on graphical processing units (GPUs). Furthermore, they lend themselves to the simulation of heterogeneous material, with a minimum of added complexity. We present the mathematical framework of assembly-free FEM approaches, through which we summarize the benefits of GPU computation. We discuss our implementation using the OpenCL computing framework, and show how it is further adapted for use on multiple GPUs. We compare the performance of single and dual GPUs implementations of our method with previous GPU computing strategies from the literature and a CPU sparse matrix approach. The utility of the novel method is demonstrated through the solution of a real-world coefficient inverse problem that requires thousands of transient heat flow simulations, each of which involves solving a 1 million degree of freedom linear system over hundreds of time steps.

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Section: Background and Motivationmentioning

confidence: 99%

Section: Preconditioned Conjugate Gradientmentioning

confidence: 99%

Analysis of heterogeneous computing approaches to simulating heat transfer in heterogeneous material

Loeb

Earls

2019

Journal of Parallel and Distributed Computing

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“…The use of GPU computing for solving the system of equations of linear elasticity problems using matrix-free and Jacobi PCG methods already has shown its advantages for FGFEA in [38]. In this work, the performance of the solving stage is evaluated using a matrix-free PCG method with two different precon- foreach i = 1 :…”

Section: Fixed-grid Finite Element Analysis (Fgfea)mentioning

confidence: 99%

“…The use of a regular grid permits to calculate and store the common elemental stiffness matrix at the finest grid K e 0 only once at the beginning of the optimization, whereas the global matrix K at the finest grid can be calculated "on-the-fly" using the design fraction of elements d for each analysis. This reduces meaningfully the use of device memory and permits to exploit the data locality [38]. Such an approach is enough for the Jacobi preconditioning but the geometric multigrid preconditioner requires the assembled coefficients at the coarser levels, which are computationally intensive to calculate "on-the-fly" and require significant memory resources when they are stored.…”

Section: Fixed-grid Finite Element Analysis (Fgfea)mentioning

confidence: 99%

“…On the one hand, a fine-grained GPU implementation of matrix-free PCG solver for structural analysis using the Fixed-Grid FEA (FGFEA) method is proposed. This technique permits to exploit data locality maximizing the GPU performance for FEA [38]. The matrix-vector multiplication operations of PCG GPU instance are performed at the Degree of Freedom (DoF) level, which allows reducing and balancing the workload for all the threads of the MPP architecture [26,39].…”

Section: Introductionmentioning

confidence: 99%

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GPU acceleration for evolutionary topology optimization of continuum structures using isosurfaces

Martnez-Frutos

Herrero-Prez

2017

Computers & Structures

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Evolutionary topology optimization of three-dimensional continuum structures is a computationally demanding task in terms of memory consumption and processing time. This work aims to alleviate these constraints proposing a well-suited strategy for Graphics Processing Unit (GPU) computing. Such a proposal adopts a fine-grained GPU instance of matrix-free iterative solver for structural analysis and an efficient GPU implementation for isosurface extraction and volume fraction calculation. The performance of the solving stage is evaluated using two preconditioning techniques, including the comparison with the sparse-matrix CPU implementation. The proposal is evaluated using topology optimization problems for real-world applications.

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Accelerating the finite element analysis of functionally graded materials using fixed‐grid strategy on CUDA‐enabled GPUs

Pikle

Sathe

Vyavahare

2019

Concurrency and Computation

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Fixed-grid discretization strategy is proposed for static structural Finite Element Analysis (FEA) of Functionally Graded Materials (FGM). The fixed-grid strategy reduces numerical integration cost dramatically by generating a single local stiffness matrix for isotropic materials. For FGMs, domain is discretized into the layers in such a way that material properties in each layer are constant. Therefore, for each layer, a single local stiffness matrix will be constructed. These matrices are directly used in the solver phase of the assembly-free FEM without constructing the global stiffness matrix. The fixed-grid strategy reduces the global memory transactions on the GPU by storing these elemental matrices in on-chip shared memory or cached constant memory.Furthermore, the assembly-free method is adopted to leverage a fine grained parallelism on the GPU at the degree of freedom level. Numerical experiments showed the effectiveness of the discrete layered approach for FGM using the fixed-grid strategy. For performance evaluation two strategies using global memory and shared memory are compared and found that the use of shared memory can achieve approximately 2.4 times better performance than global memory.

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Efficient matrix-free GPU implementation of Fixed Grid Finite Element Analysis

Cited by 29 publications

References 47 publications

Analysis of heterogeneous computing approaches to simulating heat transfer in heterogeneous material

Analysis of heterogeneous computing approaches to simulating heat transfer in heterogeneous material

GPU acceleration for evolutionary topology optimization of continuum structures using isosurfaces

Accelerating the finite element analysis of functionally graded materials using fixed‐grid strategy on CUDA‐enabled GPUs

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